Two-warehouse inventory model for deteriorating items with partial backlogging and advance payment scheme

Advance payment has a great influence on making the optimal decision in an inventory system. Two-warehouse inventory system is another imperative factor in inventory analysis. Due to competitive marketing situation, the position of a warehouse performs a significant role in business strategy. Generally, retailers want to find a shop in a popular marketing place. So, they need an additional store room due to insufficient space in a popular marketplace. Also, we have considered the advance payment scheme which is made by equal installment up to n times before receiving the products. Using all of these concepts in together, we have developed a two-warehouse inventory model for deteriorating items with advanced payment scheme. Shortages are allowed with a constant partial backlogging rate. Demand of the product is dependent on selling price. We have presented this physical problem in mathematically and solved. Also, we proved the optimality mathematically as well as graphically and proposed one theorem in order to show the optimality in theoretically. We have supplied a numerical example to illustrate the proposed inventory model. To validate the numerical result of the proposed model, we have plotted 2D and 3D graphs by using MATLAB and observed these satisfy the numerical result. Finally, we have performed sensitivity analysis changing one parameter and keeping others the same.